After cleaning with acetone, try sealing the surface with shellac.  It
might still ooze if you leave it to get hot in the sun, but it might adhere
enough to feel alright during use?  I've got many oiled old tools, but
almost all oils eventually polymerize over time.  Very few don't, so it
would be interesting to find out what was used.  Old timers used to dump
handles into containers of raw linseed for days at a time, and they
eventually got hard coatings embedded into the wood (mallet heads etc).
    Is it possibly a wax that is melting in the heat?
Cheers from Waterloo (in the first thunderstorm of the season)
Claudio

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